Final answer:
The constant of proportionality is 25 and the value of m when n = 1/5 and p = 4 is 1.25.
None of the given options is correct
Step-by-step explanation:
To solve this problem, we can use the relationship given: m varies directly with n and inversely with p. This relationship can be expressed as the equation:
m = k * (n/p)
where m represents the value of m, n represents the value of n, p represents the value of p, and k is the constant of proportionality.
1. Calculating the constant of proportionality (k):
Given that when m = 10, n = 2, and p = 5, we can substitute these values into the equation to solve for k:
10 = k * (2/5)
To solve for k, we can multiply both sides of the equation by 5/2:
10 * (5/2) = k * (2/5) * (5/2)
25 = k
Therefore, the constant of proportionality (k) is 25. This indicates that when n/p is multiplied by 25, it will yield the value of m.
2. Calculating the new value of m:
Now, we need to find the value of m when n = 1/5 and p = 4, using the constant of proportionality (k) we just calculated.
m = k * (n/p)
m = 25 * (1/5)/(4)
Simplifying the equation:
m = 25 * (1/5 * 1/4)
m = 25 * (1/20)
m = 25/20
m = 5/4
m = 1.25
Therefore, the value of m when n = 1/5 and p = 4 is 1.25.
It appears that none of the provided options (b) m = 2.5, c) m = 20, or d) k = 2) match the correct answer based on the given relationships and calculations.